Question

if (a +2b+C), (a-c) and
(a-2b+c).
are in Countinud proportion
Show that b is the mean
propostional between a and b​

Answer 1

(a +2b+C): (a-c)::(a-c):(a-2b+c)

(a +2b+C)/ (a-c)= (a-c)/(a-2b+c)

(a +2b+C)(a-2b+c)= (a-c) (a-c)

a²-2ab+ac+2ab-4b²+2bc+ac-2bc+ c² = (a-c)²

a²+ 2ac -4b²+c²= a²+c²-2ac

4ac= 4b²

ac= b²

ac= b×b

a/b = b/c

This proves that b is the mean proportion between a and c

Answer 2

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